Mathematics
OpenStudy (anonymous):

You are trying to compare the Fahrenheit and Celsius scales and you have two examples: Temperature A is 50 degrees Celsius and 122 degrees Fahrenheit. Temperature B is 100 degrees Celsius and 212 degrees Fahrenheit. What graph models the relationship between the Fahrenheit and Celsius scales? What is an equation of the line in slope-intercept form?

OpenStudy (jack1):
OpenStudy (anonymous):

I still don't get it can you help me

OpenStudy (jack1):

sure, you have a graph, and you have 2 points like so|dw:1380705932382:dw|:

OpenStudy (jack1):

|dw:1380705986692:dw|

OpenStudy (jack1):

so x axis represents degrees celsius y axis represents degrees farenheit and our 2 points are (50, 122) and (100, 212) following ok so far?

OpenStudy (anonymous):

yep:)

OpenStudy (jack1):

cools, so the only equation we can solve with only 2 points is the equation of a STRAIGHT LINE... (note: if we had 3 points we could solve a quadratic, 4points a cubic...etc) so the equation of a straight line is ...@cutegirl ? y = ???

OpenStudy (anonymous):

y=5/9x+32 right?

OpenStudy (jack1):

yeah, but we have to solve it, not know it already... ;D so eqn of a straight line is always: y = mx + c where m = gradient and c = y intercept ( y point when x = o)

OpenStudy (jack1):

so to solve m: m = (y2 - y1) / (x2 - x1) = ...?

OpenStudy (anonymous):

100-50/212-122=50=90=5/9 right?

OpenStudy (jack1):

nope, our x values were 100 and 50... not our y values... so flip it

OpenStudy (anonymous):

ow so 9/5

OpenStudy (jack1):

perfect now we have the value for m = 9/5 so we need to find c (y intercept) ... so our equation so far is: y = mx + c y = (9/5) x + c so how do we find c? @cutegirl ?

OpenStudy (anonymous):

can you help me im new with this lol

OpenStudy (jack1):

of course, happy to so if our equation's y = (9/5) x + c so to find c now, we need values for x and y (then the only unknown we are left with is c) so we can use any point that is on our line and we already know 2 points that are on our line [remember "our 2 points are (50, 122) and (100, 212) "] so pick either of those points and sub it into the equation

OpenStudy (jack1):

also, points are always written (x , y) if that helps

OpenStudy (anonymous):

212,100 122,50

OpenStudy (jack1):

ok so our equation is: y = (9/5) x + c and the point along this line that we'll use is: (50, 122) as this is an (x, y) point/pair so y = (9/5) x + c 122 = (9/5)* 50 + c can you solve for c from here?

OpenStudy (anonymous):

90?

OpenStudy (anonymous):

32 i mean

OpenStudy (jack1):

122 = (9/5)* 50 + c 122 = 90 + c 122 - 90 = c = 32, yep, perfect

OpenStudy (anonymous):

thanks you :))

OpenStudy (jack1):

so the slope intercept form of the relationship between farenheit (y) and celcius (x) is y = (9/5)x + 32

OpenStudy (jack1):

all good hey, welcomes